import java.util.ArrayList;
/**
* Your implementation of a max heap.
*
* @author YOUR NAME HERE
* @userid YOUR USER ID HERE
* @GTID YOUR GT ID HERE
* @version 1.0
*/
public class MaxHeap<T extends Comparable<? super T>> {

// DO NOT ADD OR MODIFY THESE INSTANCE/CLASS VARIABLES.
public static final int INITIAL_CAPACITY = 13;

private T[] backingArray;
private int size;

/**
* Creates a Heap with an initial capacity of INITIAL_CAPACITY
* for the backing array.
*
* Use the constant field provided. Do not use magic numbers!
*/
public MaxHeap() {
   backingArray = (T[])new Comparable[INITIAL_CAPACITY];
}

/**
* Creates a properly ordered heap from a set of initial values.
*
* You must use the BuildHeap algorithm that was taught in lecture! Simply
* adding the data one by one using the add method will not get any credit.
* As a reminder, this is the algorithm that involves building the heap
* from the bottom up by repeated use of downHeap operations.
*
* The data in the backingArray should be in the same order as it appears
* in the passed in ArrayList before you start the Build Heap Algorithm.
*
* The backingArray should have capacity 2n + 1 where n is the
* number of data in the passed in ArrayList (not INITIAL_CAPACITY from
* the interface). Index 0 should remain empty, indices 1 to n should
* contain the data in proper order, and the rest of the indices should
* be empty.
*
* @param data a list of data to initialize the heap with
* @throws IllegalArgumentException if data or any element in data is null
*/
public MaxHeap(ArrayList<T> data) {

   if(data == null){
         throw new IllegalArgumentException("data is null");
   }

   backingArray = (T[])new Comparable[2*data.size()+1];
   int index = 1;
   for(T t: data) {
         if(t == null) {
            throw new IllegalArgumentException("data is null");
         }else {
            backingArray[index++] = t;
         }
   }
   size = index-1;
   for(int i=backingArray.length/2; i > 0; i--){
         maxHeapify(i);
   }

}

/**
* Adds an item to the heap. If the backing array is full and you're trying
* to add a new item, then double its capacity.
*
* @throws IllegalArgumentException if the item is null
* @param item the item to be added to the heap
*/
public void add(T item) {

   if(item == null){
         throw new IllegalArgumentException("Cannot insert null data into data structure.");
   }

   if(size+1 >= backingArray.length){
         T[] newArray

We are going to move from fixed data already in the program which i...